Generalized swap-with-parent schemes for self-organizing sequential linear lists

Abstract

Self organizing linear search algorithms have been in the literature for over 30 years, and numerous schemes have been proposed during that time. Among all the previous algorithms, the move-to-front rule and the transposition rule are the most extensively analyzed schemes. Recently we proposed and thoroughly analyzed a new scheme, the swap-with-parent rule, which views the list as a heap structure with no ordering constraints between parents and their children [12]. From the analyses of the transposition rule and the swap-with-parent rule, it can be seen that the fundamental property of the corresponding Markov chain being time reversible greatly simplifies the analysis of the algorithm. In this paper, we shall show the existence of a class of time reversible Markov chains resulting from performing swaps on “implicit” trees (called ss_trees) which generalize and extend the results concerning the transposition and the swap-with-parent heuristics.

This paper introduces a generalization of the transposition rule and the swap-with-parent rule — the swap-with-parent-in-an-ss tree heuristic and its modification — the move-to-parent-in-an-sstree heuristic. De tailed expressions for the asymptotic probabilities and the asymptotic search cost of the scheme have been derived.

Partially supported by the National Sciences and Engineering Research Council (NSERC) of Canada